Question

A stock does not currently pay a dividend.

It is expected to pay a dividend of $2.00 five years from today. This dividend is then expected to grow at a rate of 8% for the following 5 years. It will then level off and grow at a rate of 5% indefinitely. For the next 5 years, R = 10%. R = 8% for the following 4 years and then R = 6% indefinitely. What is the expected stock price today?

Answer 1

According to Dividend discount model, the current value of stock is equal to present value of all future dividends.

According to constant growth model, price of stock is given as under

P0 = D1/(r-g) where P0 is price today, D1 is dividend in year 1 , r is discount rate and g is growth rate.

Using appropriate rate for the given time, stock price today is given as under

P0 = 2/(1.1^5) + 2*1.08/[(1.1^5)*(1.08)] + 2*1.08^2/[(1.1^5)*(1.08^2)] + 2*1.08^3 /[(1.1^5)*(1.08^3)] + 2*1.08^4/[(1.1^5)*(1.08^4)] +2*1.08^5/[(1.1^5)*(1.08^4)*1.06] + 2*1.08^5*1.05/[(0.06-0.05)*(1.1^5)*(1.08^4)*1.06]

The first term is D5 or dividend at year 5 and so on till last term where Constant growth model is applied on D11 or dividend at year 11.

P0 = 1.2418 + 1.2418 + 1.2418 + 1.2418 + 1.2653 + 132.8537

P0 = 139.0862

Thus, the stock price is $139.

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